Decimals After Fractions: The Right Order to Teach Place Value at Home

Decimals After Fractions: The Right Order to Teach Place Value at Home

A decimal is a fraction written in a different form. The 0.3 your child sees on a price tag means 3/10, and 0.47 means 47/100. When children learn decimals as a new set of rules, they make mistakes like saying 0.45 is bigger than 0.5 "because 45 is bigger than 5." When they learn decimals as fractions with denominators of 10, 100, and 1,000, that mistake mostly goes away. Here's a step-by-step order you can follow at home, with the actual numbers to use at each step.

Why Fractions Come First

The US Common Core standards follow this order. In grade 4, standard 4.NF.5 asks children to rewrite 3/10 as 30/100. Only after that does 4.NF.6 introduce decimal notation, 0.3 and 0.30. Then 4.NF.7 asks them to compare decimals to the hundredths place. The decimal point is just a shorthand for a denominator the child already understands.

Before you start on decimals, check two skills. Can your child explain why 1/2 = 5/10? Can they shade 7 out of 10 equal parts and call it 7/10? If they can't do both yet, spend another week on fractions. Pushing ahead at this point usually means you'll have to back up later.

The Five-Stage Order

StageWhat the child doesExampleReady to move on when
1. Tenths as fractionsNames parts of a whole cut into 104 of 10 strips shaded = 4/10Can shade any fraction from 1/10 to 10/10
2. Tenths as decimalsWrites the same amount with a decimal point4/10 = 0.4Converts both directions without help
3. HundredthsUses a 10×10 grid and money47/100 = 0.47 = 47 centsExplains why 0.4 = 0.40
4. ComparingRewrites decimals with the same denominator0.6 = 60/100 vs 0.58 = 58/100Orders 4 decimals correctly
5. Other fractions to decimalsBuilds equivalent fractions over 10 or 1001/4 = 25/100 = 0.25Converts 1/2, 1/4, 3/4, 1/5 on sight

Stages 1–3: Building Tenths and Hundredths

Start with a paper strip folded or ruled into 10 equal sections. Have your child shade 3 sections and write 3/10. Then show them that 0.3 says the same thing: the first place after the decimal point counts tenths. Do 10 of these in one sitting, mixing directions. Sometimes give "0.7," and they shade. Sometimes shade 2 sections, and they write both 2/10 and 0.2.

For hundredths, switch to a 10×10 grid of 100 squares. Shade one full column (10 squares) and ask for the fraction. The answer can be 10/100 or 1/10. Written as decimals, that's 0.10 and 0.1, which are the same amount. This one grid shows why a zero added at the end of a decimal doesn't change its value. Coins help too. A dollar is 100 cents, so $0.75 is 75/100 of a dollar, and a dime is 0.10, one tenth of a dollar.

Stage 4: A Worked Comparison

Here's a full example to try at home. Put these in order from smallest to largest: 0.5, 0.45, 0.405, 0.54.

  • Step 1: Find the most decimal places. 0.405 has three, so use thousandths.
  • Step 2: Rewrite each one over 1,000. 0.5 = 500/1000, 0.45 = 450/1000, 0.405 = 405/1000, 0.54 = 540/1000.
  • Step 3: Compare the whole-number numerators: 405 < 450 < 500 < 540.
  • Step 4: Write the answer in decimal form: 0.405, 0.45, 0.5, 0.54.

A child who skips Step 2 will often put 0.5 first because "5 is the smallest number." Rewriting with the same denominator turns the problem into comparing whole numbers, which they already know how to do. Once they get 5 problems like this right in a row, let them drop Step 2 and line up the digits by place instead.

Stage 5: Converting Other Fractions

Some fractions need one extra move before they become decimals. For 3/4, ask: "What times 4 makes 100?" The answer is 25, so 3/4 = 75/100 = 0.75. For 2/5, multiply top and bottom by 2 to get 4/10 = 0.4. For 7/20, multiply by 5 to get 35/100 = 0.35. Have your child memorize these four first: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75, 1/5 = 0.2. They come up all the time in money and measurement.

Save fractions like 1/3 for later. No whole number times 3 gives 10, 100, or 1,000, so 1/3 turns into the repeating decimal 0.333…. That makes more sense once your child learns long division with decimals, usually around grade 6.

A Weekly Practice Plan

Plan on about one week per stage, with 10 to 15 minutes a day. Day 1 introduces the model (strip, grid, or coins). Days 2–4 use 10 mixed problems each. Day 5 is a check: 10 problems with no hints. If your child gets 9 or more right, move to the next stage. If they get fewer, repeat Days 2–4 with new numbers. At this pace, five stages take about five to six weeks.

If you need ready-made practice sets for each stage, you can print free Korean-style drill sheets in English at mathsignal.co.kr/sheet/en.

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